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Global periodicity conditions for maps and recurrences via normal forms
dc.contributor.author | Cima Mollet, Anna |
dc.contributor.author | Gasull Embid, Armengol |
dc.contributor.author | Mañosa Fernández, Víctor |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III |
dc.date.accessioned | 2014-01-09T09:00:21Z |
dc.date.available | 2014-01-09T09:08:57Z |
dc.date.created | 2013-11 |
dc.date.issued | 2013-11 |
dc.identifier.citation | Cima, A.; Gasull, A.; Mañosa, V. Global periodicity conditions for maps and recurrences via normal forms. "International journal of bifurcation and chaos", Novembre 2013, vol. 23, núm. 11, p. 1350182-1-1350182-18. |
dc.identifier.issn | 0218-1274 |
dc.identifier.uri | http://hdl.handle.net/2117/21188 |
dc.description.abstract | We face the problem of characterizing the periodic cases in parametric families of rational diffeomorphisms of K, where K is ℝ or ℂ, having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two- and three-dimensional classes of polynomial or rational maps. In particular, we find the global periodic cases for several Lyness-type recurrences. |
dc.language.iso | eng |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals |
dc.subject.lcsh | Differential equations |
dc.subject.lcsh | Differentiable dynamical systems |
dc.subject.other | Periodic orbits |
dc.subject.other | Normal forms |
dc.subject.other | Maps |
dc.subject.other | Difference Equations |
dc.title | Global periodicity conditions for maps and recurrences via normal forms |
dc.type | Article |
dc.subject.lemac | Equacions diferencials |
dc.subject.lemac | Sistemes dinàmics diferenciables |
dc.contributor.group | Universitat Politècnica de Catalunya. CoDAlab - Control, Modelització, Identificació i Aplicacions |
dc.identifier.doi | 10.1142/S0218127413501824 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory |
dc.subject.ams | Classificació AMS::39 Difference and functional equations::39A Difference equations |
dc.subject.ams | Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory |
dc.relation.publisherversion | http://www.worldscientific.com/doi/abs/10.1142/S0218127413501824 |
dc.rights.access | Open Access |
local.identifier.drac | 12920000 |
dc.description.version | Postprint (author’s final draft) |
local.citation.author | Cima, A.; Gasull, A.; Mañosa, V. |
local.citation.publicationName | International journal of bifurcation and chaos |
local.citation.volume | 23 |
local.citation.number | 11 |
local.citation.startingPage | 1350182-1 |
local.citation.endingPage | 1350182-18 |
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